Full Practice Exam 6 — Module 1

Questions in this quiz (22)

1. Luis saves money by depositing a fixed amount into his savings account each week. The function $$g(w)=250+40w$$ gives the amount of money, in dollars, in Luis’s savings account after $$w$$ weekly deposits. What is the best interpretation of $$40$$ in this context?

   • After 40 weeks, the amount of money in Luis’s savings account was $250.
   • Each week, the amount of money in Luis’s savings account increases by $$40$$.
   • Before Luis made any weekly deposits, the amount of money in his savings account was $40.
   • Luis made a total of 40 weekly deposits.

2. The given equation relates the distinct positive real numbers $$a,b,$$ and $$m$$.$$\frac{18a}{5b}=3\sqrt{m+4}$$Which equation correctly expresses $$m$$ in terms of $$a$$ and $$b$$?

   • $$m=\frac{6a}{5b}-4$$
   • $$m=\sqrt{\frac{36a^2}{25b^2}}-4$$
   • $$m=\frac{36a^2}{25b^2}-4$$
   • $$m=\frac{6a^2}{5b^2}-4$$

3. The expression $$6x^2+bx-28,$$ where $$b$$ is a constant, can be rewritten as $$(px+q)(x+r)$$ where $$p,q,r$$ are integer constants. Which of the following must be an integer?

   • $$\frac{b}{p}$$
   • $$\frac{b}{q}$$
   • $$\frac{28}{p}$$
   • $$\frac{28}{q}$$

4. A right triangle has side lengths $$3\sqrt{3},4\sqrt{3},\sqrt{75}$$ units. What is the area of the triangle, in square units?

   • $$18\sqrt{3}$$
   • $$18$$
   • $$24\sqrt{3}$$
   • $$24$$

5. The expression $$4\sqrt[3]{2^6x^9}\cdot\sqrt[4]{8x^2}$$ is equivalent to $$ax^b,$$ where $$a$$ and $$b$$ are positive constants and $$x$$ > $$1$$. What is the value of $$a+b$$?

   • $$2^{\frac{19}{4}}$$
   • $$4^{\frac{19}{4}}$$
   • $$2^{\frac{33}{4}}$$
   • $$4^{\frac{7}{2}}$$

6. Point $$P$$ is the center of a circle. The measure of arc $$AB$$ on this circle is $$140^\circ$$. What is the measure, in degrees, of its associated angle $$\angle APB$$?

   • $$\frac{5}{4}\pi$$
   • $$\frac{1}{2}\pi$$
   • $$\frac{3}{4}\pi$$
   • $$\frac{7}{9}\pi$$

7. $$y=x^2-10x+21$$$$y=2x+b$$In the system of equations above, $$b$$ is a constant. The graphs of the equations intersect at exactly one point $$(x,y)$$ in the $$xy$$-plane. What is the value of $$x$$?

   • 6
   • Answer

8. Function $$g$$ is defined by $$g(x)=-c^x+d,$$ where $$c$$ and $$d$$ are constants. In the $$xy$$-plane, the graph of $$y=g(x)-10$$ has a $$y$$-intercept at $$(0,-\frac{48}{5}).$$ The product of $$c$$ and $$d$$ is $$\frac{24}{5}.$$ What is the value of $$c$$?

   • $$\frac{24}{7}$$
   • $$\frac{7}{5}$$
   • $$\frac{24}{5}$$
   • $$\frac{11}{5}$$

9. In the $$xy$$-plane, a parabola has vertex $$(4,-9)$$ and intersects the $$x$$-axis at $$2$$ points. If the equation of the parabola is written in the form:$$y=ax^2+bx+c,$$where $$a,$$ $$b,$$ and $$c$$ are constants, which of the following could be the value of $$a+b+c$$?

   • $$-19$$
   • $$-16$$
   • $$-11$$
   • $$0$$

10. For the linear function $$g,$$ the table shows three values of $$x$$ and their corresponding values of $$g(x).$$Which equation defines $$g(x)$$?

    • $$g(x)=4x+14$$
    • $$g(x)=14x+18$$
    • $$g(x)=22x+14$$
    • $$g(x)=18x+22$$

11. Right triangles $$ABC$$ and $$DEF$$ are similar, where $$A$$ corresponds to $$D$$, and both triangles have a right angle at $$C$$ and $$F$$, respectively. The measure of angle $$B$$ is $$22^\circ$$. Triangle $$DEF$$ is a reduced copy of triangle $$ABC$$, and the length of hypotenuse $$AB$$ is twice the length of hypotenuse $$DE$$. What is the measure, in degrees, of angle $$E$$?

    • $$11^\circ$$
    • $$22^\circ$$
    • $$44^\circ$$
    • $$46^\circ$$

12. The graph of $$8x-12y=24$$ is translated up $$3$$ units in the $$xy$$-plane. What is the $$x$$-coordinate of the $$x$$-intercept of the resulting graph?

    • $$\frac{2}{3}$$
    • $$-2$$
    • $$3$$
    • $$-\frac{3}{2}$$

13. $$x^2-4x-12=0$$One solution of the equation above can be written in the form $$2+\sqrt{k},$$ where $$k$$ is a constant. What is the value of $$k$$?

    • $$2$$
    • $$4$$
    • $$6$$
    • $$16$$

14. The equation $$3c+4d=72$$ describes the relationship between the number of cats $$c$$ and the number of dogs $$d$$ that a pet shelter can care for in one day. If the shelter cares for $$12$$ dogs in one day, how many cats can it care for that day?

    • $$4$$
    • $$8$$
    • $$12$$
    • $$24$$

15. A machine fills bottles at a constant rate. In the first $$12$$ minutes, the machine fills $$240$$ bottles. After that, the machine continues operating at the same rate, but $$20$$ bottles are removed every $$5$$ minutes due to quality checks. How many bottles are added to the total output during the next $$15$$ minutes?

    • $$120$$
    • $$150$$
    • $$180$$
    • $$240$$

16. A store raises the price of a backpack from $$60$$ to $$75$$. What is the percent increase in the price of the backpack?

    • $$20\%$$
    • $$22.5\%$$
    • $$25\%$$
    • $$27.5\%$$

17. In a right triangle, $$\cos\phi=\frac{5}{13}$$ for an acute angle $$\phi$$. What is $$\sin\phi$$?

    • $$\frac{1}{13}$$
    • $$\frac{8}{13}$$
    • $$\frac{5}{13}$$
    • $$\frac{12}{13}$$

18. For which values of $$x$$ does the inequality$$-3(2x-5)+4\le5x+1$$ hold true?

    • $$x \ge \frac{18}{11}$$
    • $$x \ge 2$$
    • $$x\ge\frac{14}{11}$$
    • $$x\ge\frac{11}{14}$$

19. A sports drink is made by mixing water and syrup in a ratio of $$5:2$$. If you have $$45$$ ounces of water, how many ounces of syrup are needed?

    • $$18$$
    • $$23$$
    • $$27$$
    • $$22$$

20. The ordered set $$\{4,6,10,14,x\}$$ contains five numbers. If the mean of the set is equal to the median, which of the following could be the value of $$x$$?

    • $$14$$
    • $$15$$
    • $$16$$

21. A group of students voted on five after-school activities. The bar graph shows the number of students who voted for each activity. How many students chose Activity $$3$$?

    • $$40$$
    • $$42$$
    • $$45$$
    • $$35$$

22. The scatterplot shows the relationship between variables $$x$$ and $$y$$. A line of best fit is drawn for the data. What is the best estimate of the $$y$$-value when $$x=6$$ based on the line of best fit?

    • $$2$$
    • $$3$$
    • $$4$$
    • $$5$$